使用 genextreme 和 weibull_min 将 Weibull 拟合到分布

Question

使用 SciPy，我试图从 this question 重现 weibull 拟合。当我使用genextreme 函数时，我的配合看起来不错，如下所示：

import numpy as np
from scipy.stats import genextreme
import matplotlib.pyplot as plt

data=np.array([37.50,46.79,48.30,46.04,43.40,39.25,38.49,49.51,40.38,36.98,40.00,
               38.49,37.74,47.92,44.53,44.91,44.91,40.00,41.51,47.92,36.98,43.40,
               42.26,41.89,38.87,43.02,39.25,40.38,42.64,36.98,44.15,44.91,43.40,
               49.81,38.87,40.00,52.45,53.13,47.92,52.45,44.91,29.54,27.13,35.60,
               45.34,43.37,54.15,42.77,42.88,44.26,27.14,39.31,24.80,16.62,30.30,
               36.39,28.60,28.53,35.84,31.10,34.55,52.65,48.81,43.42,52.49,38.00,
               38.65,34.54,37.70,38.11,43.05,29.95,32.48,24.63,35.33,41.34])

shape, loc, scale  = genextreme.fit(data)

plt.hist(data, normed=True, bins=np.linspace(15, 55, 9))

x = np.linspace(data.min(), data.max(), 1000)
y = genextreme.pdf(x, shape, loc, scale)
plt.plot(x, y, 'c', linewidth=3)

参数为：(0.44693977076022462, 38.283622522613214, 7.9180988170857374)。形状参数是正的，对应于Weibull wikipedia page 上形状参数的符号，据我所知，它相当于 R 中的负形状参数？

看来genextreme 自己决定分发是 Gumbel、Frechet 还是 Weibull。这里它选择了 Weibull。

现在我正在尝试使用 weibull_min 函数重现类似的拟合。我基于this post 尝试了以下方法，但参数看起来与我使用genextreme 得到的非常不同：

weibull_min.fit(data, floc=0) 

现在的参数是：(6.4633107529634319, 0, 43.247460728065136)

0 是形状参数吗？如果分布是 Weibull，肯定应该是正数？

Answer 1

weibull_min.fit()返回的参数为(shape, loc, scale)。 loc 是位置参数。 （所有 scipy 分布都包含一个位置参数，即使是那些通常不使用位置参数的分布。）weibull_min.fit 的文档字符串包括：

Returns
-------
shape, loc, scale : tuple of floats
    MLEs for any shape statistics, followed by those for location and
    scale.

您使用了参数floc=0，因此，正如预期的那样，fit(data, floc=0) 返回的位置参数为 0。